The area between the curves is obviously the integral. You can see that the area is broken into 2 parts. To find out where they intersect, it's best to use a graphing calculator to find the point. x2 = ex cannot easily be solved using algebra. The intersection point is approx x = -.703467. So you can divide the integrals into 2 parts, from -1 to -0.703467 and in that integral do ∫(x2 - ex)dx then in the second integral from -0.703467 to 1 and in that integral do ∫(ex - x2)dx and add the results together.